This study aims to analyse the nature of the dynamical exchange correlation field in the Hubbard-Holstein model. The goal being to find the dependence of such a field on the model parameters much like in analogy with Density Functional Theory. In order to do so, we begin by studying the analytical solutions of simple systems, such as the Hubbard dimer and small Holstein systems. This will then be used as a reference point for a numerical analysis of the exchange correlation field in the Hubbard-Holstein model. From this, one expects to be able to deduce a general form of such a field and find a correlation between the Hubbard, the Holstein, and the Hubbard-Holstein model.
We describe a quantum simulator for the Hubbard-Holstein model (HHM), comprising two dressed Rydberg atom species held in a monolayer by independent painted potentials, predicting that boson-mediated preformed pairing and Berezinskii-Kosterlitz-Thouless (BKT) transition temperatures are experimentally accessible. The HHM is important for modeling the essential physics of unconventional superconductors. Experimentally realizable quantum simulators for HHMs are needed (1) since HHMs are difficult to solve numerically and analytically, (2) to explore how competition between electron-phonon interactions and strong repulsion affects pairing in unconventional superconductors, and (3) to understand the role of boson-mediated local pairing in pseudogaps and fermion condensates. We propose and study a quantum simulator for the HHM, using optical lattices, painted using zeros in the ac Stark shift, to control two Rydberg atom species independently within a monolayer. We predict that interactions are sufficiently tunable to probe (1) both HHMs and highly unconventional phonon-mediated repulsions, (2) the competition between intermediate-strength phonon- and Coulomb-mediated interactions, and (3) BKT transitions and preformed pairing that could be used to examine key hypotheses related to the pseudogap. We discuss how the quantum simulator can be used to investigate boson-mediated pairing and condensation of fermions in unconventional superconductors.
We study the interplay between the electron-phonon
(e-ph) and on-site electron-electron (e-e) interactions in a three-orbital Hubbard-Holstein model on an extended one-dimensional lattice using determinant quantum Monte Carlo. For weak e-e and
e-ph interactions, we observe a competition between an orbital-selective Mott phase (OSMP) and a (multicomponent) charge-density-wave (CDW) insulating phase, with an intermediate metallic phase located between them. For large e-e and
e-ph couplings, the OSMP and CDW phases persist, while the metallic phase develops short-range orbital correlations and becomes insulating when both the e-e and
e-ph interactions are large but comparable. Many of our conclusions are in line with those drawn from a prior dynamical mean-field theory study of the two-orbital Hubbard-Holstein model [Phys. Rev. B 95, 121112(R) (2017)] in infinite dimension, suggesting that the competition between the
e-ph and e-e interactions in multiorbital Hubbard-Holstein models leads to rich physics, regardless of the dimension of the system.